# setcov

##### Set Covariance of a Window

Computes the set covariance function of a window.

##### Usage

`setcov(W, V=W, ...)`

##### Arguments

- W
- A window (object of class
`"owin"`

. - V
- Optional. Another window.
- ...
- Optional arguments passed to
`as.mask`

to control the pixel resolution.

##### Details

The set covariance function of a region $W$ in the plane is the function $C(v)$ defined for each vector $v$ as the area of the intersection between $W$ and $W+v$, where $W+v$ is the set obtained by shifting (translating) $W$ by $v$.

We may interpret $C(v)$ as the area of the set of
all points $x$ in $W$ such that $x+v$ also lies in
$W$.
This command computes a discretised approximation to
the set covariance function of any
plane region $W$ represented as a window object (of class
`"owin"`

, see `owin.object`

). The return value is
a pixel image (object of class `"im"`

) whose greyscale values
are values of the set covariance function.

The set covariance is computed using the Fast Fourier Transform,
unless `W`

is a rectangle, when an exact formula is used.

If the argument `V`

is present, then `setcov(W,V)`

computes the set *cross-covariance* function $C(x)$
defined for each vector $x$
as the area of the intersection between $W$ and $V+x$.

##### Value

- A pixel image (an object of class
`"im"`

) representing the set covariance function of`W`

, or the cross-covariance of`W`

and`V`

.

##### See Also

##### Examples

```
w <- owin(c(0,1),c(0,1))
v <- setcov(w)
plot(v)
```

*Documentation reproduced from package spatstat, version 1.31-3, License: GPL (>= 2)*